The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A144097 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A144097

The 4-Schroeder numbers: a(n) = number of lattice paths (Schroeder paths) from (0,0) to (3n,n) with unit steps N=(0,1), E=(1,0) and D=(1,1) staying weakly above the line y = 3x.
(history; published version)

#92 by Michael De Vlieger at Tue Jan 09 11:03:25 EST 2024

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reviewed

approved

#91 by Stefano Spezia at Tue Jan 09 11:03:03 EST 2024

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proposed

reviewed

#90 by Michael De Vlieger at Tue Jan 09 10:59:54 EST 2024

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editing

proposed

#89 by Michael De Vlieger at Tue Jan 09 10:59:53 EST 2024

LINKS

Lin Yang, Yu-Yuan Zhang, and Sheng-Liang Yang, <a href="https://doi.org/10.1016/j.laa.2023.12.021">The halves of Delannoy matrix and Chung-Feller properties of the m-Schröder paths</a>, Linear Alg. Appl. (2024).

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approved

editing

#88 by Joerg Arndt at Wed Aug 09 11:39:24 EDT 2023

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reviewed

approved

#87 by Michel Marcus at Wed Aug 09 11:21:19 EDT 2023

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proposed

reviewed

#86 by Seiichi Manyama at Wed Aug 09 10:02:30 EDT 2023

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editing

proposed

#85 by Seiichi Manyama at Wed Aug 09 08:14:11 EDT 2023

FORMULA

a(n) = (1/n) * Sum_{k=0..n-1} (-1)^k * 2^(n-k) * binomial(n,k) * binomial(4*n-k,n-1-k) for n > 0. - Seiichi Manyama, Aug 09 2023

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approved

editing

#84 by R. J. Mathar at Tue Jul 18 09:09:27 EDT 2023

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editing

approved

#83 by R. J. Mathar at Tue Jul 18 09:09:20 EDT 2023

FORMULA

Conjecture: D-finite with recurrence 3*n*(3*n-1)*(3*n+1)*(35*n^2-98*n+68) *a(n) +(-15610*n^5+67123*n^4-106824*n^3+77633*n^2-25514*n+3000)*a(n-1) +3*(n-2) *(3*n-4) *(3*n-5) *(35*n^2-28*n+5) *a(n-2)=0. - R. J. Mathar, Sep 06 2016

STATUS

approved

editing